A Stretching Coordinates System/Reductive perturbation theory

Ahmer ali
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why stretching coordinate transformation is used in the study of solitons formation using reductive perturbation theory?
What is the physical reason behind the usually used transformation of the form mentioned below
transformation.JPG
 
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Please link to the specific paper in question.
 
So I know that electrons are fundamental, there's no 'material' that makes them up, it's like talking about a colour itself rather than a car or a flower. Now protons and neutrons and quarks and whatever other stuff is there fundamentally, I want someone to kind of teach me these, I have a lot of questions that books might not give the answer in the way I understand. Thanks
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